We describe a new search for diffuse ultra-high-energy gamma-ray emiss
ion associated with molecular clouds in the Galactic disk. The Chicago
Air Shower Array (CASA), operating in coincidence with the Michigan m
uon array (MIA), has recorded over 2.2 x 10(9) air showers from 1990 A
pril 4 to 1995 October 7. We search for gamma rays based upon the muon
content of air showers arriving from the direction of the Galactic pl
ane. We find no significant evidence for diffuse gamma-ray emission, a
nd we set an upper limit on the ratio of gamma rays to normal hadronic
cosmic rays at less than 2.4 x 10(-5) at 310 TeV (90% confidence limi
t) from the Galactic plane region: (50 degrees < l < 200 degrees; -5 d
egrees < b < 5 degrees). This limit places a strong constraint on mode
ls for emission from molecular clouds in the Galaxy. We rule out signi
ficant spectral hardening in the outer Galaxy, and conclude that emiss
ion from the plane at these energies is likely to be dominated by the
decay of neutral pions resulting from cosmic-ray interactions with pas
sive target gas molecules.